# Push-Pull Optimization of Quantum Controls

## TL;DR

This paper introduces push-pull optimization, a novel quantum control method that enhances convergence by incorporating orthogonal operators into the objective function, demonstrated through simulations and NMR experiments.

## Contribution

It proposes a new push-pull optimization technique for quantum control that improves convergence and performance over traditional methods.

## Key findings

- Significantly improved convergence in optimization routines.
- Successful application to quantum control of coupled qubits.
- Experimental demonstration with NMR techniques.

## Abstract

Quantum optimal control involves setting up an objective function that evaluates the quality of an operator representing the realized process w.r.t. the target process. Here we propose a stronger objective function which incorporates not only the target operator but also a set of its orthogonal operators. We find significantly superior convergence of optimization routines with the combined influences of all the operators. We refer to this method as the $\textit{push-pull}$ optimization. In particular, we describe adopting the push-pull optimization to a gradient based approach and a variational-principle based approach. We carry out extensive numerical simulations of the push-pull optimization of quantum controls on a pair of Ising coupled qubits. Finally, we demonstrate its experimental application by preparing a long-lived singlet-order in a two-qubit system using NMR techniques.